Reflections on Beauty in Motion

Matt Strassler [February 21, 2012]

Why does the sight of the Moon draw our gaze and silence our voices? What is it about the planets, those exceptionally bright points of light that wander among the stars, that we instinctively find so beautiful? Is it perhaps that they make us dream of faraway, unreachable places? Is it that they are beacons in the night, nature’s candle flames, helping keep fear at bay, and offering us hope amid darkness? Or is it perhaps that they seem to float — we do love things that float, whether they be autumn leaves, balloons, clouds or birds — suspended in the sky, in apparent defiance of the force of gravity which keeps us pinned to the Earth?

This last thought offers a certain delicious irony… for in truth the planets and the Moon, in their procession above our heads, obey gravity’s dictates.

The next few days, weather permitting, will give us a chance to contemplate these questions. Our planet’s natural satellite, on its monthly trip around the Earth, will pass three of the brighter planets in the sky, creating one lovely spectacle after another. Of course, the Moon really passes nowhere near the planets, just as your outstretched hand, when it blocks your view of the Moon, is nowhere near the Moon itself. It is all a matter of perspective — of geometry, of cavernous spaces, of the play of light, and of the elegant choreography of the solar system. But this perspective is not something we sense easily. Our eyes can perceive no depth for objects so far away, and so our brains form a two-dimensional picture from the three dimensions of the universe, projecting the Moon, the planets and the stars, at extraordinary distances from one another, onto a psychologically flat black screen of the night sky. It takes great mental effort to see things as they are, and not as they appear. This, too, is worthy of contemplation.

On the night of February 22nd, just after sunset (don’t be late!), one of the most delicate of nocturnal sights awaits: a fragile fingernail Moon, so thin that it seems it would break if you could touch it. This happens only twice about every four weeks, one day just before sunrise, and then, two days later, just after sunset. Why? Simple geometry, and reflected light.

[Note: all dates and times in this article are appropriate for the United States and its neighbors. If you live on other continents, the phenomena described here will still occur, but may be shifted later by one calendar day, and may appear slightly different in detail. Please consult a sky-watching website that is aimed at your region of the globe.]

The Moon and planets give off no light of their own; they merely reflect the light of the Sun. Whatever we see of them, however bright they are, is determined by how much sunlight they reflect back to us. And this amount is all merely a matter of geometry, a consequence of where the Moon and planets are relative to the Sun and the Earth. If you think about this for a bit, and arm yourself with a rather small telescope, you can even determine to your complete satisfaction that what you’ve learned in school is really true: that the Moon orbits the Earth, while the planets all orbit the Sun, with two of them closer than Earth, and the rest further away.

To convince yourself that the Moon orbits the Earth actually requires no telescope; it just requires paying a bit of attention to a few facts that you already know, but may not have put together. We all know the Moon has “phases” — periods during the four weeks of a lunar cycle when it is full, or half, or crescent-shaped. But have you noticed these phases follow a very strict and simple pattern? A crescent Moon is always seen just after sunset, or just before sunrise; on such a night the Moon is only visible for an hour or two. A half Moon is always overhead either at sunrise or at sunset, and is visible half the night. A full Moon is visible all night, rises when the Sun sets, sets when the Sun rises, and is overhead at midnight.

The phases of the moon arise from the overlap between the half of the moon that faces the sun (which is lit by sunlight, indicated by lighter colors) and the half of the moon that faces the earth (which is the part that we can see, to the earthward side of the red lines.) When the moon lies roughly between the earth and the sun, very little of the lit side of the moon can be seen, and the moon is a crescent; when the earth lies roughly between the moon and the sun, the lit side and visible side are the same, and the moon is full. Distances are not to scale.

And have you noticed that the lit portion of the Moon always is on the side nearest the Sun? If it is evening and the Moon is visible, the lit portion of the Moon always faces to the west (which is down toward the horizon when the Moon is setting), whereas if the Moon is visible after midnight the lit portion always faces to the east (which is down when the Moon is rising).

Meanwhile, the Moon’s size in the sky never changes very much (other than an optical illusion when it approaches the horizon that makes it appear larger — take a photo and you’ll find it isn’t really bigger.) The top and bottom tips of the crescent Moon are the same distance apart in the sky as is the top and bottom of the full Moon. You can also confirm this if you are lucky enough to spot the lovely phenomenon of “earthshine,” which you are most likely to see after the moon leaves twilight but before it becomes too bright — which happens during the few days after the evening fingernail Moon, so look for it this week. Earthshine arises from light that bounces off the lit portion of the Earth, travels to the unlit portion of the Moon, and back down to the dark parts of the Earth to be admired — a faint glow of the dark portion of the Moon that reveals that even a crescent Moon is still a sphere, and the same size as a full Moon.

Earthshine is doubly reflected light: from the sun to the sunlit part of earth, out to the dark part of the moon, and from there to the night portion of the earth, where it may be admired.

These things tell us that the Moon’s distance from the Earth never changes very much; and that during a full Moon, the Earth stands between the Moon and the Sun, while the Moon lies nearly between the Earth and the Sun when it form a crescent. This means that the Moon travels in an orbit around the Earth, at a (nearly) constant distance from the Earth, with a cycle of about four weeks. Oh, and meanwhile, the fact that a little sliver of sunlit Moon forms a crescent shape, just like the skin on a wedge of an orange, confirms the Moon is a sphere.

By contrast, the two planets Venus and Mercury appear initially quite peculiar, in terms of what they do in the sky. Neither is ever directly overhead at night; in fact at the hour of midnight you’ll never find either of them anywhere in the sky.

Have you ever seen Mercury? Unless you’ve actively looked for it, you probably haven’t. In order to observe Mercury, you have to look either right after sunset, or just before sunrise — but not both on the same day, or even the same month. And on February 22nd — if you look soon after sunset, no more than 30 minutes or so, and if you have a clear horizon, with no nearby trees or buildings and no clouds or high mountains to your west, you will find (here’s a sky map), several Moon-widths to the left of the setting fingernail Moon, a pinprick of light, all by itself. That’s Mercury — mercurial indeed, for it is dim in the twilight, and will soon set. (You can look again later in the week if you miss it on the 22nd; Mercury will still be there, though the Moon will have moved on and won’t be there to guide you. Binoculars will be helpful in finding it.)

Mercury and Venus, with orbits closer to the sun than Earth's, can never appear overhead at night; they set soon after the sun, or rise not long before. The angle they can make with the horizon at sunrise or sunset cannot be larger than shown in this figure (not to scale). At its highest Venus can be seen much higher in the evening sky than Mercury can be, indicating Mercury lies closer to the sun. Distances and angles only approximate; sizes of sun and planets not to scale.

Why is it so hard to find Mercury? Because it has an orbit around the Sun that is much closer to the Sun than Earth’s orbit, and this assures that it never can appear far from the Sun in the sky, and must either set just after the Sun does, or rise just before it. As it orbits the Sun (and as the Earth does too) it moves, from Earth’s perspective, from behind the Sun (when we can’t possibly see it) to the side of the Sun that puts it into the evening sky at sunset, but not very far; then it passes between the Sun and the Earth (when the bright Sun makes it impossible for us to observe it) and from there into the morning sky, but again not very far, and then finally it retreats behind the Sun to begin its cycle anew.

Venus is easier to see for several reasons. First, it is bigger than Mercury; it is almost the same size as Earth. Second, while Mercury is greyish, Venus is bright white; it has an atmosphere (with a horrific greenhouse-gas effect that keeps its surface much hotter than an oven) which is eternally overcast with white clouds, making the planet highly reflective. Third, its orbit is further from the Sun than is Mercury’s, and that has two effects: Venus comes closer to the Earth than does Mercury, which makes it appear larger and brighter, and it moves higher into the sky than does Mercury, meaning that it is visible sometimes for several hours after sunset or before sunrise (though again, for the same reasons as Mercury, not both at the same time). This makes it possible to observe without any special effort. Inevitably, every time it brightens, calls come in to the police about a UFO: a surprisingly bright Unidentified Floating Object, a.k.a. Venus.

But the real clincher that tells you that Venus (and Mercury) orbit the Sun, and not the Earth, is this: they have phases too, like the Moon, but with key differences. As they go through their phases, they change size, unlike the Moon, and they are brightest not when they are full, like the Moon, but when they are in a wide crescent phase (not quite at the fingernail stage.) In fact, what happens is this: first Venus appears in the evening sky, dim, but fully lit; then over successive weeks, it rises high in the evening sky, becomes larger, brighter, but is no longer fully lit; then it begins to fall back toward the horizon in the evening, but still becoming brighter and larger, while approaching a crescent shape, and finally, with a thin crescent but quite large indeed, it disappears in post-sunset twilight. Then it appears a few days later in the pre-sunrise twilight, as a thin crescent, and the second half of the cycle occurs in the early morning hours, reversing the sequence of the evenings’ festivities in front of a smaller audience. (Here is a nice perspective drawing [not to scale!] illustrating the phases as they would be predicted to occur if Venus orbits the Sun.)

A planet (such as Mercury or Venus) with an orbit that is smaller than Earth's has phases like the moon but grows and shrinks during its orbit round the sun due to its changing distance from earth. The portion of the planet visible from Earth is to the earthward side of the red lines; the lit portion is shown in yellow. Such a planet is always largest when a crescent and smallest when full, and is brightest sometime in between. Distances are not to scale; the planet is drawn large to make its appearance easier to see.

Unfortunately this is something you cannot verify with the naked eye — and arguably this is what delayed the recognition that Venus orbits the Sun for many thousands of years. It was only the telescope of Galileo, almost exactly 400 years ago, that revealed that Venus’s phases are as I have just described. (Here is an image from Galileo’s notebooks, showing at bottom the phases and size of Venus; and here is a composite of photos showing how Venus’s appearance changes over time.) You only need a very small telescope, just enough to magnify objects about 20 times, or even a powerful set of binoculars (if your eyes are good, skies are very clear, and you are patient enough to let your eyes fully adjust to darkness), to verify what Galileo saw.

Venus is now in the middle of the evening part of the cycle. Still more than half lit, and still brightening, growing in size, becoming gradually less fully illuminated by the Sun, and climbing day by day relative to the evening horizon, it is a spectacular sight on its own and will become more so over the next months. If you pay attention week by week you will see Venus reach its highest point relative to the horizon in about a month, before turning back and approaching the Sun, from Earth’s perspective. (In fact, on June 5th and 6th, Venus will pass in front of the Sun’s disk! A “transit!” Mark it in your calendar.)

On February 25th, the Moon will pass close by Venus. It should be the most spectacular event of the week. Think, when you see these two great orbs in the sky — Earth’s spouse and Earth’s sibling — about what your brain refuses to tell you. Despite the Moon’s apparent immensity, and the dot that is Venus, the planet is actually five times wider than the Moon (and about the same size as Earth), and appears smaller and dimmer only because it is currently (though this will decrease over the coming months) about four hundred times further away.

And think of this, too. The light from the Moon travels from the Sun (a journey of about eight and a half minutes, so great are the distances), bounces off the Moon and travels to Earth (a journey of nearly a second and a half) while the light from Venus must first travel from the sun, under six minutes, bounce off of Venus, and travel (currently) over eight additional minutes to reach Earth. It’s just like the delay of an echo; when you hear thunder from a lightning strike in the mountains, you may hear it first directly, then hear it again as the sound bounces off a distant peak. If someone could turn off the Sun with a light-switch, you’d see the Moon go dark eight minutes later, but Venus would continue to glow in the sky for another six minutes or so after that, before winking out.

Light that comes to earth via the Moon travels a much shorter distance than light that first reflects off Venus, or off of Jupiter. Distances not to scale.

And what about Jupiter? The solar system’s largest planet would continue to glow for well over an hour! For that is how long it takes for sunlight first to reach Jupiter (it orbits about five times further from the Sun than does Earth) and then, reflecting off of it, to travel to Earth (for it is currently about five times further away from Earth than is Venus).

This week you will find Jupiter above Venus in the sky, closer to overhead. And late on February 26th, the Moon will pass nearby, completing the week’s drama. Jupiter is a much bigger planet than Earth or Venus — about ten times larger in radius — so in a telescope or good binoculars (which are enough to show that it is not a point but a disk against the night sky) it appears to be twice as wide right now as does Venus, despite being five times further away. Yet though it appears larger, it still appears dimmer than Venus. Why? As you go further from the Sun, the Sun’s light is dispersed more greatly, so that the Sun would appear much dimmer and smaller at Jupiter than it does at Earth, while at Venus the Sun would appear larger and brighter. This means that relatively less sunlight is reflected off Jupiter’s huge surface. But do not let your mind be fooled when on the 26th you see Jupiter dwarfed and outshined by the Moon. Remember that the interior of this gaseous giant could hold a thousand Earths.

That Jupiter orbits the Sun, and that its distance from the Sun is much greater than Earth’s, is again something you can recognize with a small telescope, or even binoculars. Unlike Venus and the Moon, Jupiter has (essentially) no phases; it is always almost completely lit by sunlight, from our point of view. The same is true of Saturn, by the way (and also of Uranus and Neptune, which require binoculars or a telescope for you to observe them easily in the first place), and, to a slightly lesser extent, of Mars. All of these planets, unlike Venus and Mercury, can be overhead at midnight, and what’s more, those are the nights in which they appear largest and brightest. They are smallest and dimmest when they are only visible in the sky just after sunset or just before sunrise.

What explains these patterns? An object is overhead at midnight when the Earth lies between it and the Sun, as we saw for the full moon. And that is when these planets are closest to the Earth. When they are visible only just after sunset, they are very, very far from Earth, with the Sun almost in between them and the Earth, and so they are quite dim because of their great distance from our planet. And meanwhile, since they never pass between the Earth and the Sun, they can never become crescents in the sky the way the Moon, Mercury and Venus do. (To see how Jupiter changes size as it orbits the Sun, look at the upper panel of photographs in this image.)

A planet with an orbit farther out than the Earth's (including Mars, Jupiter, Saturn, Uranus and Neptune) is always near to fully lit, but grows and shrinks as its distance from Earth changes, and is overhead at midnight when it is closest, largest and brightest. Distances are not to scale; the planet is drawn large to make its appearance easier to see.

So if you obtain a small telescope, you may enjoy following along for a year or so as the elegant dance of planets and the Moon goes through its steps; watch the planets grow and shrink as they approach and recede; note how they rise or fall in our two-dimensional sky, and how this reflects their three-dimensional motion (and the Earth’s) through space; and observe the phases of Venus and how they confirm that it orbits the Sun. And you may reflect on how a small advance in technology around the year 1609 boosted Galileo’s vision just enough to allow him to discover so many previously unknown features of the Moon, Sun and planets, and forever alter humanity’s view of ourselves and of our neighbors in the heavens.

But even without a telescope — even with just your eyes, or small binoculars to help them — you can enjoy the beauty of the night sky this week, and immerse yourself in the immensity of our home. And there is more to come: you can watch Mars reach its overhead-at-midnight position, and glow about as bright as it can, on March 3rd; and meanwhile Venus climbs night by night in the evening sky, while Jupiter seems to hover in place, bringing them close together around March 13th for yet another spectacular pairing. (To see where the planets are or will be located around the sun, try this site; and to see how they appear or will appear from earth or elsewhere, try this one.)

The crescent Moon, as it moves around the earth from lower right toward the upper left, will appear to pass near to Mercury, Venus and Jupiter over several days, beginning February 22nd. Distances and angles not to scale..

This Saturday, when the Moon brushes past Venus, I will be thinking of one of my favorite personal encounters with nature. It happened a few years ago, during a solitary summer visit to the National Volcanic Monument that surrounds Mount Saint Helens, the volcano in southern Washington state that blew off its top in 1980. From a ridge to the north, facing the gaping hole in the mountain’s side and the sweeping, devastated valley down below it, I watched the rocks turn a golden grey in the sunset, and waited as the stars appeared and the sky turned mostly to black. In the west, Venus glowed brightly, a pearl above and to the left of a pendant crescent Moon, earthshine completing its disk. Then I heard a snuffling sound, seemingly quite close. I thought it must be a small animal in the brush behind me, but when I reached the brush I heard the sound again, from somewhere else. Puzzled, I looked up, and froze. Grazing on the hillock less than fifty yards away, silhouetted against the last orange glow of sunset, were three majestic antlered elk.

Lazily they ate their fill, while above them — behind them — beyond them hung the Moon, Venus, and the stars, beckoning to the unfathomable.

Dear Professor, thanks for your blog. I can’t remember if I mentioned this in the discussion about the canal and barge analogy to hidden dimensions. But I wonder what it was like for early astronomers to deduce the mechnics of the heavens? Must have been much like those boats.

Beautifully written. Made me remember how once I was lying on dock, looking at first few stars appear in the early evening sky. I noticed several bright points coming close together, they looked exactly the same. One was a star, another satellite, the third clearly a plane judging by their movements. But I could never figure out the forth one which moved erratically, zigzagged at what appeared to be tremendous speed. Only when I got up and my point of view shifted, I realize that it was a seed flying in the air just a few meters above me.

It´s 3:46 a.m. here, As I couldn´t sleep any longer I just jumped onto my computer and started checking my emails looking for some entertainment and voila! there it was another beautifully written exiting article on your blog.
I´ve been following your blog for a few months with great pleasure and, tonight it has been a like that magic elixir I just needed tonight.
Thank you so much for creating this blog and sharing your observations, they´re deeply appreciated.

Thanks for some other useful internet site. The area different could I get that will variety of information and facts printed in this great way? I own a difficult task that we’re just now implementing, and I’ve been in the style outside for similarly info.